$2.$ Bill Clinton reportedly was paid $$15$ million to write his book My Life. Suppose the book took three years to write. In the time he spent writing, Clinton could have been paid to make speeches. Given his popularity, assume that he could earn $$8$ million per year $($paid at the end of the year$)$ speaking instead of writing. Assume his cost of capital is $10\%$ per year.

a$.$ What is the NPV of agreeing to write the book $($ignoring any royalty payments$)?$

b$.$ Assume that, once the book is finished, it is expected to generate royalties of $$5$ million in the first year $($paid at the end of the year$)$ and these royalties are expected to decrease at a rate of $30\%$ per year in perpetuity. What is the NPV of the book with the royalty payments?